Transcript NEUTRINO OSCILLATIONS

NEUTRINO OSCILLATIONS
Luigi DiLella
Marienburg Castle
August 2002
Content of these lectures:
1. Short introduction to neutrinos
2. Formalism of neutrino oscillations in vacuum
3. Solar neutrinos:
Production
Results
Formalism of neutrino oscillations in matter
Future experiments
4. Atmospheric neutrinos
5. LSND and KARMEN experiments
6. Oscillation searches at accelerators:
Long baseline experiments
Short baseline experiments
7. Long-term future
8. Conclusions
Neutrinos in the Standard Model
Measurement of the Z width at LEP: only three light neutrinos (ne, nm, nt)
Neutrino mass mn = 0 “by hand”
two-component neutrinos:
helicity (spin component parallel to momentum) = – 1 for neutrinos
p
+ 1 for antineutrinos
p
n:
n:
spin
helicity +1 neutrinos
helicity –1 antineutrinos
spin
do not exist
If mn > 0 helicity is not a good quantum number
(helicity has opposite sign in a reference frame moving faster than the neutrino)
massive neutrinos and antineutrinos can exist in both helicity states
Are neutrinos Dirac or Majorana particles?
Dirac neutrinos: n  n
lepton number is conserved
Examples: neutron decay N  P + e– + ne
pion decay p+  m+ + nm
Majorana neutrinos: n  n (only one four-component spinor field)
lepton number is NOT conserved
Neutrinoless double–b decay: a way (the only way?) to distinguish Dirac from
Majorana neutrinos
(A, Z)  (A, Z+2) + e– + e–
violates lepton number conservation
can only occur for Majorana neutrinos
A second-order weak process:
n
ne
n
p
e–
p
e–
two neutrons
of the same nucleus
Process needs neutrino helicity flip between emission and absorption
(neutron decay emits positive helicity neutrinos, neutrino capture by
neutrons requires negative helicity)
neutrinoless double–b decay can only occur if m(ne) > 0
Transition Matrix Element m(ne)
The most sensitive search for double-b decay:
76Ge  76Se
–
–
E (e–1) + E (e–2) = 2038 keV
32
34 + e + e
Heidelberg–Moscow experiment:
Five enriched 76Ge crystals (solid–state detectors)
Total mass: 19.96 kg , 86% 76Ge
(natural Germanium contains only 7.7% 76Ge)
Crystals are surrounded by anticoincidence
counters and installed in underground
Gran Sasso National Laboratory (Italy)
Search for mono–energetic line at 2038 keV
No evidence for neutrinoless double-b decay:
m(ne) < 0.2 eV for Majorana neutrinos
Neutrino mass: relevance to cosmology
A prediction of Big Bang cosmology: the Universe is filled with a Fermi gas of neutrinos
at temperature T  1.9 K. Density ~60 n cm–3 , 60 n cm–3 for each neutrino type (ne, nm, nt)
Critical density of the Universe :
H0: Hubble constant (Universe
2
3H 0
2
present expansion rate)
ρc 
 1.05 10 4 h0 eV/cm 3
H0 = 100 h0 km s–1 Mpc –1 (0.6 < h0 <0.8)
8pGN
GN: Newton constant
Neutrino energy density (normalized to rc):
n 
rn
1
2

m
c

2
n
rc 94h0 n
n = 1 for 30 eV   mn c 2  60 eV
n
Recent evidence from the study of distant Super-Novae:
rc consists of ~30% matter (visible or invisible) and ~70% “vacuum energy”
Cosmological models prefer non-relativistic dark matter (easier galaxy formation)
with rn  20% of matter density
cosmological limit on neutrino masses
 mn c 2  4 eV
n
Direct measurements of neutrino masses
ne: mc2 < 2.5 eV (from precise measurements of the electron energy spectrum from 3H decay)
nm: mc2 < 0.16 MeV (from a precise measurement of m+ momentum from p+ decay at rest)
nt: mc2 < 18.2 MeV (from measurements of t  nt + 3, 5 or 6 p at LEP)
With the exception of ne direct measurements of neutrino masses have no sensitivity
to reach the cosmologically interesting region
Neutrino interaction with matter
W–boson exchange: Charged–Current (CC) interactions
Quasi-elastic scattering
n e + n  e– + p
n e + p  e+ + n
nm + n  m– + p nm + p  m+ + n
Energy threshold: ~112 MeV
nt + n  t – + p
nt + p  t + + n
Energy threshold: ~3.46 GeV
Cross-section for energies >> threshold: sQE  0.45 x 10–38 cm2
Deep-inelastic scattering (DIS) (scattering on quarks, e.g. nm + d  m– + u)
ne + N  e– + hadrons
ne + N  e+ + hadrons
(N: nucleon)
nm + N  m– + hadrons
nm + N  m+ + hadrons
nt + N  t – + hadrons
nt + N  t+ + hadrons
Cross-sections for energies >> threshold: sDIS(n)  0.68E x 10–38 cm2 (E in GeV)
sDIS( n )  0.5 sDIS(n)
Z–boson exchange: Neutral–Current (NC) interactions
Flavour-independent: the same for all three neutrino types
n + N  n + hadrons
n + N  n + hadrons
Cross-sections:
Very low cross-sections:
sNC( n)  0.3 sCC(n)
mean free path of a 10 GeV nm  1.7 x 1013 g cm–2
sNC( n )  0.37 sCC( n)
equivalent to 2.2 x 107 km of Iron
0.8
Suppression of t production
by nt CC interactions
from t mass effects
sCC(nt)
sCC(nm)
0.6
0.4
0.2
Neutrino – electron scattering
ne
n
e–
0
20
40
60
80
100
E (n) [GeV]
Cross-section: s = A x 10–42 E cm2 (E in GeV)
W
Z
e
(all three
n types)
e
–
0.0
ne
(ne only)
ne: A  9.5
nm, nt: A  1.6
ne : A  3.4
nm, nt : A  1.3
Note: cross-section on electrons is much smaller than cross-section on nucleons
because s  GF2 W2 (W  total energy in the centre-of-mass system) and W2  2meEn
NEUTRINO OSCILLATIONS
The most promising way to verify if mn > 0
(Pontecorvo 1958; Maki, Nakagawa, Sakata 1962)
Basic assumption: neutrino mixing
ne, nm, nt are not mass eigenstates but linear superpositions
of mass eigenstates n1, n2, n3 with masses m1, m2, m3, respectively:
n   Ui n i
i
Ui: unitary mixing matrix
n i  Vi n 

Vi  (Ui )
*
 = e, m, t (“flavour” index)
i = 1, 2, 3 (mass index)
Time evolution of a neutrino state of momentum p
created as n at time t=0
n (t )  eipr Uk e iE t n k
Note:
k
n (0)  n
k
Ek  p  mk
2
2
phases e
iEk t
are different if mj  mk
appearance of neutrino flavour nb  n at t > 0
Case of two-neutrino mixing
n  cos n1  sin  n 2
  mixing angle
n b   sin  n1  cos n 2
For nn at production (t = 0):
i (pr  E1t )
n (t )  e
cos n
1
e
i ( E2  E1 )t
sin  n 2

Probability to detect nb at time t if pure n was produced at t = 0
Pb (t )  nb n(t )
2
Note: for m << p
m 2t
 sin (2) sin (
)
4E
2
2
E
Natural units:
  c 1
m2  m22 – m12
2
m
p 2  m2  p 
2p
(in vacuum!)
m2 2  m12 m22  m12 m2
E2  E1 


2p
2E
2E
Use more familiar units:
L
Pb ( L)  sin (2) sin (1.267 m )
E
2
2
2
L = ct distance between
neutrino source and detector
Units: m2 [eV2]; L [km]; E [GeV] (or L [m]; E [MeV])
NOTE: Pb depends on m2 and not on m. However, if m1 << m2
(as for charged leptons and quarks), then m2  m 22  m12  m22
Define oscillation length l:
E
l  2.48 2
m
Units: l [km]; E [GeV]; m2 [eV2]
(or l [m]; E [MeV])
Pb ( L)  sin (2 ) sin (p
2
Smaller E, larger m2
2
L
l
)
Larger E, smaller m2
sin2(2)
Distance from neutrino source
Disappearance experiments
Use a beam of n and measure n flux at distance L from source
Measure
P  1 
 Pb
b 
Examples:
 Oscillation experiments using ne from nuclear reactors
(En  few MeV: under threshold for m or t production)
 nm detection at accelerators or from cosmic rays
(to search for nm nt oscillations if En is under threshold
for t production)
Main uncertainty: knowledge of the neutrino flux for no oscillation
the use of two detectors (if possible) helps
n source
Near detector
measures n flux
n beam
Far detector
measures P
Appearance experiments
Use a beam of n and detect nb (b  ) at distance L from source
Examples:
 Detect ne + Nucleon  e- + hadrons in a nm beam
 Detect nt + Nucleon  t - + hadrons in a nm beam
(Energy threshold  3.5 GeV)
NOTES
nb contamination in beam must be precisely known
(ne/nm  1% in nm beams from high-energy accelerators)
Most neutrino sources are not mono-energetic but have wide
energy spectra. Oscillation probabilities must be averaged over
neutrino energy spectrum.
Under the assumption of two-neutrino mixing:
 Observation of an oscillation signal
allowed region m2 versus sin2(2)
upper limit to Pb (Pb < P)
 Negative result
exclusion region
Large m2  short l
Average over source and detector size:
Pb ( L)  sin 2 (2 ) sin 2 (p
Small
m2
L
1
)  sin 2 (2 )
l
2
 long l: sin(p
(
Pb  P  1.6 m
)
2 2
L
l
) p
L
l
 L
2
sin (2 ) 
E
log(m2)
2
(the start of the first oscillation)
0
sin2(2)
1
PARAMETERS OF OSCILLATION SEARCH EXPERIMENTS
Neutrino source
Flavour
Baseline L
Sun
ne
1.5 x 108 km
Cosmic rays
nm ne
nm ne
10 km 
13000 km
20 m 
250 km
15 m 
730 km
Nuclear reactors ne
Accelerators
nm ne
nm ne
Energy
0.2 15 MeV
0.2 GeV 
100 GeV
Minimum m2
1011 eV2
104 eV2
<E>  3 MeV 101  106 eV2
20 MeV 
100 GeV
103  10 eV2
EVIDENCE/HINTS FOR NEUTRINO OSCILLATIONS
 Solar Neutrino Deficit: ne disappearance between Sun and Earth
 Atmospheric neutrino problem: deficit of nm coming from the other side
of the Earth
 LSND Experiment at Los Alamos: excess of ne in a beam consisting mainly
of nm , ne and nm
SOLAR NEUTRINOS
Birth of a visible star: gravitational contraction of a cloud of
primordial gas (mostly 75% H2, 25% He)
increase of
density and temperature in the core
ignition of nuclear fusion
Balance between gravity and pressure
hydrostatic equilibrium
Final result from a chain of fusion reactions:
4p  He4 + 2e+ + 2ne
Average energy produced in the form of electromagnetic radiation:
Q = (4Mp – MHe4 + 2me)c2 – <E(2ne)>  26.1 MeV
(<E(2ne)>  0.59 MeV)
(from 2e+ + 2e–  4g)
Sun luminosity: L = 3.846x1026 W = 2.401x1039 MeV/s
Neutrino emission rate: dN(ne)/dt = 2 L/Q  1.84x1038 s –1
Neutrino flux on Earth: F(ne) 6.4x1010 cm–2 s –1
(average Sun-Earth distance = 1.496x1011 m)
STANDARD SOLAR MODEL (SSM)
(developed and continuously updated by J.N. Bahcall since 1960)
Assumptions:  hydrostatic equilibrium
 energy production by fusion
 thermal equilibrium (energy production rate = luminosity)
 energy transport inside the Sun by radiation
Input:  cross-sections for fusion processes
 opacity versus distance from Sun centre
Method:  choose initial parameters
 evolution to present time (t = 4.6x109 years)
 compare measured and predicted properties
 modify initial parameters (if needed)
Present Sun properties: Luminosity L = 3.846x1026 W
Radius R = 6.96x108 m
Mass M = 1.989x1030 kg
Core temperature Tc = 15.6x106 K
Surface temperature Ts = 5773 K
Hydrogen fraction in core = 34.1% (initially 71%)
Helium fraction in core = 63.9% (initially 27.1%)
as measured on
surface today
Two fusion reaction cycles
pp cycle (98.5% of L)
85%
p + p  e+ + n e + d
p + p  e+ + ne + d or (0.4%): p + e– + p  ne + d
p + d  g + He3
p + d  g + He3
He3 + He3  He4 + p + p
or (2x10-5): He3 + p  He4 + e+ + ne
15%
p + p  e+ + n e + d
p + d  g + He3
He3 + He4  g + Be7
e– + Be7  ne + Li7
p + Li7  He4 + He4
or (0.13%)
p + Be7  g + B8
B8  Be8 + e+ + ne
Be8  He4 + He4
CNO cycle (two branches)
p + N15  C12 + He4
p + N15  g + O16
p + C12  g + N13
p + O16  g + F17
N13  C13 + e+ + ne
F17  O17 + e+ + ne
p + C13  g + N14
p + O17  N14 + He4
p + N14  g + O15
O15  N15 + e+ + ne
NOTE #1: in all cycles 4p  He4 + 2e+ + 2ne
NOTE #2: present solar luminosity originates from fusion reactions which occurred
~ 106 years ago. However, the Sun is practically stable over ~ 108 years.
Expected neutrino fluxes on Earth (pp cycle)
Notations
pp : p + p  e+ + ne + d
7Be : e– + Be7  n + Li7
e
–
pep : p + e + p  ne + d
8B : B8  Be8 + e+ + n
e
3
4
hep : He + p  He + e+ + ne
Radial distributions of neutrino production
inside the Sun, as predicted by the SSM
The Homestake experiment (1970–1998): first detection of solar neutrinos
A radiochemical experiment (R. Davis, University of Pennsylvania)
ne + Cl 37  e– + Ar 37
Energy threshold E(ne) > 0.814 MeV
Detector: 390 m3 C2Cl4 (perchloroethylene) in a tank installed in the Homestake
gold mine (South Dakota, U.S.A.) under 4100 m water equivalent (m w.e.)
(fraction of Cl 37 in natural Chlorine = 24%)
Expected production rate of Ar 37 atoms  1.5 per day
Experimental method: every few months extract Ar 37 by N2 flow through tank,
purify, mix with natural Argon, fill a small proportional counter, detect radioactive
decay of Ar 37: e– + Ar 37  ne + Cl 37 (half-life t1/2 = 34 d)
(Final state excited Cl 37 atom emits Augier electrons and/or X-rays)
Check efficiencies by injecting known quantities of Ar 37 into tank
Results over more than 20 years of data taking
SNU (Solar Neutrino Units): the unit to
measure event rates in radiochemical
experiments:
1 SNU = 1 event s–1 per 1036 target atoms
Average of all measurements:
R(Cl 37) = 2.56  0.16  0.16 SNU Solar
(stat)
SSM prediction: 7.6
+1.3
–1.1
(syst)
SNU
Neutrino
Deficit
Real-time experiments using water Čerenkov counters to detect solar
neutrinos
Neutrino – electron elastic scattering: n + e–  n + e–
Detect Čerenkov light emitted by recoil electron in water (detection threshold ~5 MeV)
Cross-sections: s(ne)  6 s(nm)  6 s(nt)
W and Z exchange Only Z exchange
(5MeV electron path
in water  2 cm)
Two experiments: Kamiokande (1987 – 94). Useful volume: 680 m3
Super-Kamiokande (1996 – 2001). Useful volume: 22500 m3
installed in the Kamioka mine (Japan) at a depth of 2670 m w.e.
Verify solar origin of neutrino signal
from angular correlation between
recoil electron and incident neutrino
directions
cossun
Super-Kamiokande detector
Cylinder, height=41.4 m, diam.=39.3 m
50 000 tons of pure water
Outer volume (veto) ~2.7 m thick
Inner volume: ~ 32000 tons (fiducial
mass 22500 tons)
11200 photomultipliers, diam.= 50 cm
Light collection efficiency ~40%
Inner volume while filling
Recoil electron kinetic energy distribution from
ne – e elastic scattering of mono-energetic neutrinos
is almost flat between 0 and 2En/(2 + me/En)
convolute with predicted spectrum to obtain
SSM prediction for electron energy distribution
En
SSM prediction
Data
6
8
10
12
14
Electron kinetic energy (MeV)
Results from 22400 events (1496 days of data taking)
Measured neutrino flux (assuming all ne): F(ne) = (2.35  0.02  0.08) x 106 cm-2 s –1
SSM prediction: F(ne) = (5.05 )
Data/SSM = 0.465  0.005
+0.093
(stat) –0.074
+1.01
–0.81
(stat)
(syst)
x 106 cm-2 s –1
(including theoretical error)
ne DEFICIT
Comparison of Homestake and Kamioka results with SSM predictions
0.465  0.016
2.56  0.23
Homestake and Kamioka results were known since the late 1980’s.
However, the solar neutrino deficit was not taken seriously at that time.
Why?
The two main solar ne sources in the Homestake and water experiments:
He3 + He4  g + Be7
p + Be7  g + B8
e– + Be7  ne + Li7 (Homestake)
B8  Be8 + e+ + ne (Homestake, Kamiokande, Super-K)
Fusion reactions strongly suppressed by Coulomb repulsion
Ec
R1
d
R
Potential energy:
Z1Z2e2/d
2
Z1e
Z2
e
Z1Z2e 2 e 2 cZ1Z2 197 Z1Z2
Ec 


MeV (R1 + R2 in fm)
R1  R 2 c R1  R 2 137 R1  R 2
d
~R1+R2
Ec  1.4 MeV for Z1Z2 = 4, R1+R2 = 4 fm
Average thermal energy in the Sun core <E> = 1.5 kBTc  0.002 MeV (Tc=15.6 MK)
kB (Boltzmann constant) = 8.6 x 10-5 eV/deg.K
Nuclear fusion in the Sun core occurs by tunnel effect and depends
strongly on Tc
Nuclear fusion cross-section at very low energies
1 -2p
s (E)  e S (E)
E
Nuclear physics term difficult to calculate
measured at energies ~0.1– 0.5 MeV
and assumed to be energy independent
Z1Z2e 2
Tunnel effect:  
v = relative velocity v
Predicted dependence of the ne fluxes on Tc:
From e– + Be7  ne + Li7:
F(ne)  Tc8
From B8  Be8 + e+ + ne :
F(ne)  Tc18
F  Tc N
F/F = N Tc/Tc
How precisely do we know
the temperature T of the Sun core?
Search for ne from p + p  e+ + ne + d (the main component of the
solar neutrino spectrum, constrained by the Sun luminosity)
very little theoretical uncertainties
Gallium experiments: radiochemical experiments to search for
ne + Ga71  e– + Ge71
Energy threshold E(ne) > 0.233 MeV
reaction sensitive to solar neutrinos
from p + p  e+ + ne + d (the dominant component)
Three experiments:
In the Gran Sasso National Lab
 GALLEX (Gallium Experiment, 1991 – 1997)
150 km east of Rome
 GNO (Gallium Neutrino Observatory, 1998 – )
Depth 3740 m w.e.
 SAGE (Soviet-American Gallium Experiment)
In the Baksan Lab (Russia) under
the Caucasus. Depth 4640 m w.e.
Target: 30.3 tons of Gallium in HCl solution (GALLEX, GNO)
50 tons of metallic Gallium (liquid at 40°C) (SAGE)
Experimental method: every few weeks extract Ge71 in the form of GeCl4 (a highly volatile
substance), convert chemically to gas GeH4, inject gas into a proportional counter, detect
radioactive decay of Ge71: e– + Ge71  ne + Ga71 (half-life t1/2 = 11.43 d)
(Final state excited Ga71 atom emits X-rays: detect K and L atomic transitions)
Check of detection efficiency:
 Introduce a known quantity of As71 in the tank (decaying to Ge71: e– + Ge71  ne + Ga71)
 Install an intense radioactive source producing mono-energetic ne near the tank:
e– + Cr51  ne + V51 (prepared in a nuclear reactor, initial activity 1.5 MCurie equivalent
to 5 times the solar neutrino flux), E(ne) = 0.750 MeV, half-life t1/2 = 28 d
Ge71
production rate
~1 atom/day
SAGE (1990 – 2001)
SSM PREDICTION:
Data/SSM = 0.56  0.05
+6.5
70.8–6.1 SNU
128 +9 SNU
–7
0.4650.016
Data are consistent with:
 Full ne flux from p + p  e+ + ne + d
 ~50% of the ne flux from B8  Be8 + e+ + ne
 Very strong (almost complete) suppression
of the ne flux from e– + Be7  ne + Li7
The real solar neutrino puzzle:
There is evidence for B8 in the Sun (with deficit 50%), but no evidence for Be7;
yet Be7 is needed to make B8 by the fusion reaction p + Be7  g + B8
Possible solutions:
 At least one experiment is wrong
 The SSM is totally wrong
 The ne from e– + Be7  ne + Li7 are no longer ne when they reach the Earth and become
invisible
ne OSCILLATIONS
Unambiguous demonstration of solar neutrino oscillations: SNO
(the Sudbury Neutrino Observatory in Sudbury, Ontario, Canada)
SNO: a real-time experiment detecting Čerenkov
light emitted in 1000 tons of high purity heavy
water D2O contained in a 12 m diam. acrylic
sphere, surrounded by 7800 tons of high purity
water H2O
Light collection: 9456 photomultiplier tubes,
diam. 20 cm, on a spherical surface with a radius
of 9.5 m
Depth: 2070 m (6010 m w.e.) in a nickel mine
Electron energy detection threshold: 5 MeV
Fiducial volume: reconstructed event vertex
within 550 cm from the centre
Solar neutrino detection at SNO:
(ES) Neutrino – electron elastic scattering: n + e–  n + e–
Directional, s(ne)  6 s(nm)  6 s(nt) (as in Super-K)
(CC) ne + d  e– + p + p
Weakly directional: recoil electron angular distribution  1 – (1/3) cos(sun)
Good measurement of the ne energy spectrum (because the electron takes
most of the ne energy)
(NC) n + d  n + p + n
Equal cross-sections for all three neutrino types
Measure the total solar flux from B8  Be8 + e+ + n in the presence of
oscillations by comparing the rates of CC and NC events
Detection of n + d  n + p + n
Detect photons ( e+e–) from neutron capture at thermal energies:
 First phase (November 1999 – May 2001):
n + d  H3 + g
(Eg = 6.25 MeV)
 Second phase (in progress): add high purity NaCl (2 tons)
n + Cl 35  Cl 36 + g – ray cascade (S Eg  8. 6 MeV)
 At a later stage:
insert He3 proportional counters in the detector
n + He3  p + H3 (mono-energetic signal)
SNO expectations
Use three variables:
 Signal amplitude (MeV)
 cos(sun)
 Event distance from centre (R)
(measured from the PM relative times)
(R/Rav)3
cos(sun)
(proportional to volume)
(Rav = 6 m = radius of the acrylic sphere)
Use b and g radioactive sources to calibrate the energy scale
Use Cf252 neutron source to measure neutron detection efficiency (14%)
Neutron signal does not depend on cos(sun)
From 306.4 days of data taking:
Number of events with kinetic energy Teff > 5 MeV and R < 550 cm: 2928
Neutron background: 78  12 events. Background electrons 45 +18 events
–12
Use likelihood method and the expected distributions to extract the three signals
Solar neutrino fluxes, as measured separately
from the three signals:
FCC(ne) = 1.76
+0.06 +0.09
–0.05 –0.09
x 106 cm-2s-1
FES(n) = 2.39
+0.24 +0.12
–0.23 –0.12
x 106 cm-2s-1
FNC(n) = 5.09
+0.44 +0.46
–0.43 –0.43
stat. syst.
x 106 cm-2s-1
Note: FCC(ne)  F(ne)
Calculated under the assumption that
all incident neutrinos are ne
FSSM(n) = 5.05 +1.01 x 106 cm-2s-1
–0.81
cm–2 s –1
stat. and syst. errors
combined
FNC(n) – FCC(ne) = F(nmt) = 3.33  0.64 x
5.2 standard deviations from zero
evidence that solar neutrino flux on
106
Earth contains sizeable nm or nt component (in any combination)
Write FES(n) as a function of F(ne) and F(nmt):
1
F ES (n )  F(n e )  F(n mt )
6
1
(because s ES (n mt )  s ES (n e ) )
6
F(n) = F(ne) + F(nmt)
Interpretation of the solar neutrino data using the two-neutrino
mixing hypothesis
Vacuum oscillations
ne spectrum on Earth F(ne) = Pee F0(ne)
(F0(ne)  spectrum at production)
L [m]
L
2
2
2
ne disappearance probability P  1  sin (2)sin (1.267 m
)
E [MeV]
ee
E
m2 [eV2]
L = 1.496 x 1011 m (average Sun – Earth distance with 3.3% yearly variation
from eccentricity of Earth orbit)
Fit predicted ne spectrum to data using , m2 as adjustable parameters
4x10–10 eV2
Regions of oscillation parameters
consistent with solar neutrino
data available before the end
of the year 2000
10–10
4x10–11
(L. Wolfenstein, 1978)
NEUTRINO OSCILLATIONS IN MATTER
Neutrinos propagating through matter undergo refraction.
p: neutrino momentum
2p
Refraction index: n  1    1  2 Nf (0) N: density of scattering centres
p
f(0): forward scattering amplitude
In vacuum:
E p m
2
2
(at  = 0°)
Plane wave in matter:  = ei(np•r –Et)
2
p
E  (np)2  m2  E 

E
(for  << 1)
But energy must be conserved!
Add a term V  neutrino potential energy in matter
E  E  V
p
2p
V      Nf (0)
E
E
2
V < 0: attractive potential (n > 1)
V > 0: repulsive potential (n < 1)
Neutrino potential energy in matter
1. Contribution from Z exchange (the same for all three flavours)
n
n
Z
e,p,n
2
GF N p( 1  4 sin 2 θw )
2
GF: Fermi coupling constant
2
Np (Nn): proton (neutron) density
VZ (n)  
GF N n
2
w: weak mixing angle
VZ (p)  VZ (e) 
e,p,n
2. Contribution from W exchange (only for ne!)
ne
e
VW [eV]  2GF Ne  7.63  10
W+
e
ne
NOTE: V(n) = – V( n )
electron density
14
Z
ρ
A
matter density [g/cm3]
Example: two-neutrino mixing between ne and nm in a constant
density medium (same results for mixing between ne and nt)
 ne 
n   
 nm 
Use flavour basis:
H  ( E  VZ )
(Remember:
2
1 M ee

1 2 E M me 2
1
0
0
Evolution equation:
Hn  i
n
t
2x2 matrix
M em 2
M mm
2
 VW
1
0
0
0
M2
M2
p M  p
E
for M  p)
2p
2E
2
2
1 2
M ee  ( m  m2 cos2 )
m 2  m12  m2 2
2
2
2
2

m

m

m
1
2
1
2
2
M em  M me  m2 sin 2
2
1 2
NOTE: m1, m2,  are defined in vacuum
2
M mm  ( m  m2 cos2 )
2
2
Rewrite:
H  ( E  VZ )
1
0
2
1 M ee  2 EVW

1 2E
M me 2
0
diagonal term: no mixing
M em 2
M mm 2
term responsible for ne–nm mixing
r = constant
time-independent H
Diagonalize non-diagonal term in H to obtain mass eigenvalues and eigenstates
1 2
1
Eigenvalues
2
2
2
2 2
2
M

(
m


)

(

m
cos
2



)

(

m
)
sin
2
in matter
2
2
Z
  2EVW  1.526  10
rE [eV2]
A
7
(r in g/cm3, E in MeV)
Mixing angle in matter
m 2 sin 2
tan 2 m 
m 2 cos 2  
For  = m2cos2   res mixing becomes
maximal (m = 45°) even if the mixing angle
in vacuum is very small: “MSW resonance”
(discovered by Mikheyev and Smirnov in 1985)
Notes: MSW resonance can exist only if  < 45° (otherwise cos2 < 0)
For ne  < 0
no MSW resonance if  < 45°
Mass eigenvalues versus 
M2
M22
res  m cos2
2
M12
Oscillation length in matter:
lm  l
m 2
(m 2 cos 2   ) 2  (m 2 ) 2 sin 2 2
(l  oscillation length in vacuum)
At  =  res:
lm 
l
sin 2
Matter-enhanced solar neutrino oscillations
Solar neutrinos are produced in a high-density
medium (the Sun core) and travel through
variable density r = r(t)
Use formalism of neutrino oscillations in matter:
Evolution equation Hn = i n /  t
H (2 x 2 matrix) depends on time t through r(t)
H has no eigenstates
Solve the evolution equation numerically:
 1
(pure ne at production)
n(0)   
 0
 n 
n()  n(0)      n(0)  iH (0)n(0)
 t t 0
 n 
n(t  )  n(t )      n(t )  iH (t )n(t )
 t t
(until neutrino escapes from the Sun)
solar density
vs. radius
100
10
r
[g/cm3]
1
0.1
R/RO
0.
0.2
0.4
0.6
0.8
( = very small time interval)
It is always possible to write:
n(t )  a1 (t )n1  a2 (t )n 2
(|a1|2 + |a2|2 = 1)
where n1, n2 are the “local” eigenstates of the time-independent Hamiltonian for fixed r
At production (t=0, in the Sun core): n e  cosmn1 (0)  sin mn 2 (0)
[ 0m  m (0) ; n1(0), n2(0) eigenstates of H for r=r(0)]
0
0
Assume  (mixing angle in vacuum) < 45°: cos > sin in vacuum
m > 45° at production if  > res : a (0)  cos0  a (0)  sin 0
1
 > res
E[ MeV ] 
res 6.6  10 m cos 2

2VW
( Z / A)r
6
2
m
2
m
( m2 in eV2, r in g/cm3)
A simple class of solutions ( “adiabatic solutions”): a1  a1(0), a2  a2 (0) at all t
(if r varies slowly over an oscillation length)
At exit from the Sun (t=tE):
n(t E )  a1 (0)n1 (t E )  a2 (0)n 2 (t E )
M2
n1(tE), n2(tE) :mass eigenstates in vacuum
In vacuum
nm n 2  n e n 2
(because  < 45° in vacuum)
nm n(t E )  n e n(t E )
ne DEFICIT
m <
45°
m >
45°
Regions of the (m2 , sin22) plane allowed by the solar neutrino flux
measurements in the Homestake, Super-K and Gallium experiments
Different energy thresholds
different regions
of the (m2 , sin22) plane
Super-K
The regions common to the three measurements
contain the allowed oscillation parameters
Matter-enhanced solar neutrino oscillations (“MSW solutions”)
(using only data available before the end of the year 2000)
Survival probability
versus neutrino energy
LMA
10–5 eV 2
SMA
LOW
sin22
10–3
10–2
LMA: Large Mixing Angle
SMA: Small Mixing Angle
10–1
Super-K 2002
Data/SSM
Additional experimental information
Energy spectrum distortions
Electron kinetic energy (MeV)
SNO recoil electron spectrum
from ne + d  e– + p + p
SNO data/SSM prediction
ne deficit is energy independent within errors (no distortions)
Seasonal variation of measured neutrino flux in Super-K
Yearly variation of the Sun-Earth
distance: 3.3%  seasonal variation of
the solar neutrino flux for some vacuum
oscillation solutions
Note: expected seasonal variation from
change of solid angle  6.6%
Days since start of data taking
The observed effect is consistent
with the variation of solid angle alone
Day-night effects (expected for some MSW solutions from matter-enhanced
oscillations when neutrinos traverse the Earth at night
increase of ne flux at
night)
Subdivide night spectrum into
bins of Sun zenith angle to study
dependence on path length inside
Earth and density
ADN
DN

0.5( D  N )
cos(Sun zenith angle)
SNO Day and Night Energy Spectra
(CC + ES + NC events)
Difference Night – Day
SK data: comparison with oscillations
Electron energy
distribution
Sun zenith angle distributions
for different electron energy bins
Vacuum oscillation
SMA
LMA
LOW
 Vacuum oscillation and SMA solution disagree with electron energy distribution
 LMA and LOW solutions describe reasonably well the zenith angle distributions
 No dependence on zenith angle within errors
The present interpretation
of all solar neutrino data
using two-neutrino mixing
m2 [eV2]
Global fits to all existing solar neutrino data
48 data points, two free parameters (mixing angle , m2)  46 degrees of freedom
LMA solution: 2 = 43.5; m2 = 6.9x10– 5 eV2;  = 31.7° (BEST FIT)
LOW solution: 2 = 52.5; m2 = 7.2x10– 8 eV2;  = 39.1°
2 = 9; Prob(2  9) = 1.1% (marginally acceptable)
Note: variable tan2 is preferred
to sin22 because sin22 is symmetric
around  = 45° and MSW solutions
are possible only if  < 45°
LMA
tan2
Verification of the LMA solution using antineutrinos from nuclear reactors
Nuclear reactors: intense, isotropic sources of ne from b decay of neutron-rich
fission fragments
ne production rate: 1.9x1020 Pth s–1
(Pth [GW]: reactor thermal power)
Broad energy spectrum extending to 10 MeV, <E>  3 MeV
Uncertainty on the expected ne flux: ±2.7 %
Detection:
ne + p  e+ + n (on the free protons of hydrogen – rich liquid scintillator)
e+ e–  2g
prompt signal
E = En – 0.77 MeV
thermalization by multiple collisions
(<t> 180 ms), followed by capture
n + p  d + g (Eg  2.2 MeV)
delayed signal
KAMioka Liquid scintillator Anti-Neutrino Detector (KAMLAND)
ne source: several nuclear reactors surrounding the Kamioka site
Total power 70 GW — average distance 175  35 km (long baseline)
Expected ne flux (no oscillations)  1.3 x 106 cm–2 s–1
~550 events/year
Average oscillation length <losc>  110 km for m2 = 6.9 x 10–5 eV 2 (LMA)
expect large ne deficit with measurable energy modulation
KAMLAND detector
1000 tons liquid scintillator
Transparent balloon
Mineral oil
Acrylic sphere
Photomultipliers (1879)
(coverage: 35% of 4p)
13 m
18 m
Outer detector (pure H2O)
225 photomultipliers
KAMLAND sensitivity to ne oscillations
Fiducial mass: 600 tons
Exclusion regions
if no ne deficit
is observed
1 s regions
after 3 years
Data taking in progress since January 2002 — results expected soon
Borexino experiment (at Gran Sasso National Lab)
Study of the elastic scattering reaction
n + e¯  n + e¯
Recoil electron detection threshold = 0.25 MeV
sensitivity to from e– + Be7  ne + Li7
(En = 0.861 MeV)
300 tons of ultra-pure liquid scintillator
isotropic light emission
no directionality
Expected event rate ( electron energy 0.25 — 0.8 MeV):
No oscillations: 55 events/day
+5
events/day
–3
( 3s )
LMA: 35
Expected background: ~ 15 events/day
Start data taking: mid 2003
“ATMOSPHERIC” NEUTRINOS
Primary cosmic ray
interacts in upper
atmosphere
e
The main sources of atmospheric neutrinos:
p, K   m  + nm( nm)
 e  + ne( ne) + nm(nm)
At energies E < 2 GeV most parent particles
decay before reaching the Earth
n m  nm
2
n e  ne
At higher energies, most muons
reach the Earth before decaying:
n m  nm
 2 (increasing with E)
n e  ne
Energy range of atmospheric neutrinos: 0.1 — 100 GeV
Very low event rate: ~100 /year for a detector mass of 1000 tons
Uncertainties on calculations of atmospheric neutrino fluxes: typically ± 30%
(from composition of primary spectrum, secondary hadron distributions, etc.)
Uncertainty on the nm/ne ratio: only ±5% (because of partial cancellations)
Detection of atmospheric neutrinos
nm + Nucleon  m + hadrons: presence of a long, minimum ionizing track (the m)
ne + n  e– + p, ne + p  e+ + n : presence of an electromagnetic shower
(ne interactions with multiple hadron production is difficult to separate from neutral current events
for atmospheric ne only quasi-elastic interactions can be studied)
Particle identification in a water Čerenkov counter
muon track:
dE/dx consistent with minimum ionization
sharp edges of Čerenkov light ring
electron shower:
high dE/dx
“fuzzy” edges of Čerenkov light ring
(from shower angular spread)
42°
Measure electron/muon separation by exposing a 1000 ton water Čerenkov counter
(a small Super-K detector) to electron and muon beams from accelerators.
Probability of wrong identification ~2%
Measurements of the nm/ne ratio: first hints for a new phenomenon
Water Čerenkov counters: Kamiokande (1988), IMB (1991), Super-K (1998)
Conventional calorimeter (iron plates + proportional tubes): Soudan2 (1997)
(nm/ne)measured
R = (n /n )
m e predicted
= 0.65 ± 0.08
Atmospheric neutrino data from Super-K
Distance between event vertex and inner detector wall 1 metre
(April 96 – July 01)
PC events are all assumed to be m-like
Lepton (e/m) energy [GeV]
Classification of Super-K events
(m/e)Data
(m/e)MC
= 0.638 ± 0.016 ± 0.05
(m/e)Data
(m/e)MC
+0.030
= 0.658 –0.028 ± 0.078
An additional event sample:
Upward-going muons produced by nm interactions in the rock
Note: downward going muons are dominated by high-energy cosmic ray muons
traversing the mountain and reaching the detector
Measurement of zenith angle distribution
Definition of zenith angle :
Polar axis along the local vertical axis,
directed downwards
Down-going:  = 0º
Earth atmosphere
detector
Up-going:  = 180°
Horizontal:  = 90°
Baseline L (distance between
neutrino production point and
detector) depends on zenith angle
Earth
local vertical axis
L [Km]
104
L varies between ~10 and ~12800 km as  varies
between 0º and 180º
search for oscillations
with variable baseline
Strong angular correlation between incident neutrino
and outgoing electron/muon for E > 1 GeV:
  25° for E = 1 GeV;
n
  0 as E increases

103
102
±5 km uncertainty
on n production point
10
–1.
–0.5
0.
cos
0.5
1.
e/m
Super-K zenith angle distributions
No oscillation (2 = 456.5 / 172 degrees of freedom)
nm – nt oscillation best fit: m2 = 2.5x10–3 eV2, sin22 = 1.0
2 = 163.2 / 170 degrees of freedom
Super-K zenith angle distributions:
evidence for nm disappearance over distances of ~1000 — 10000 km
Oscillation cannot be nm – ne:
 Excluded by reactor experiment CHOOZ (see later)
 Zenith angle distribution for e-like events would show opposite sign up-down asymmetry
(more upward-going e-like events) because nm/ne  2 at production
a nm – nt oscillation is the most plausible solution
(nt + N  t + X requires E(nt) > 3.5 GeV and t  m decay fraction  18% only)
Super-K
Combined region (90% CL):
m2=(1.3 – 3.9) x 10–3 eV2
sin22 > 0.92
CHOOZ: a long baseline ne disappearance experiment
sensitive to m2 > 7 x 10–4 eV2
Two reactors at the Chooz EDF power plant (total thermal power 8.5 GW)
L = 998, 1114 m
Detector:
5 tons of Gadolinium-loaded
liquid scintillator
(neutron capture in Gd  g’s
with total energy 8.1 MeV)
17 tons unloaded scintillator
(to contain the g–rays)
90 ton liquid scintillator
(for cosmic ray rejection)
Detector installed in an
underground site
under 300 m w.e.
Data taking: 1997-98
(Experiment completed in 1998)
Event rate with reactors at full power: 25 / day
Background rate (reactors off): 1.2 / day
Positron energy spectrum
(prompt signal from ne + p  n + e+)
and comparison with expected spectrum
without oscillation
Measured spectrum
Expected spectrum (no oscillation)
Ratio (integrated over energy spectrum)
= 1.010 ± 0.028 ± 0.027
no evidence for ne disappearance
Positron energy
CHOOZ experiment
Excluded region for
ne – nx oscillations
m2
[eV2]
Super-K
nm –nt oscillation
Distinguishing nm – nt from nm – ns oscillations
(ns: “sterile” neutrino, a hypothetical neutrino with no coupling to W and Z
no interaction with matter)
Two methods:
 Select a sample of multi-ring events with no m–like ring (event sample enriched
in neutral-current events n + N  n + hadrons)
nm – nt oscillation: no up – down asymmetry in the zenith angle distribution
(nm and nt have the same neutral-current interaction)
nm – ns oscillation: up – down asymmetry similar to that of m–like events
 Matter effects when neutrinos traverse the Earth
Potential energy in matter: V(nm) = V(nt) = VZ, V(ns) = 0
nm – nt oscillation: no matter effects
2
AZ
5
nm – ns oscillation: V  
GF N n  3.8  10 r
Z
2
A
neutron density
 eV 2 
 GeV 


density [g/cm3]
(VZ < 0 for neutrinos, VZ > 0 for anti-neutrinos)
Matter-effects are important when VZEn  m2 (En  20 GeV for r  5 g/cm3)
Study high-energy m-like events
Fit Super-K data with nm – ns oscillations
No oscillation
nm–ns oscillation
(nm–nt oscillations:
2min=163.2/170 dof)
Try nm– n’ oscillation with n’ = cos nt + sin ns
pure nt
sin2 < 0.19 (90% confidence)
LSND and KARMEN experiments: search for nm – ne oscillations
Conceptual design
Anti-coincidence
counter
p±
800 Mev
protons

n
target
+ beam dump
shielding
Neutrino sources
70–90%
800 MeV
(kin. energy)
proton-nucleus
collision
p+
Decay At Rest (DAR) ~75%
Decay In Flight
(DIF) ~5%
~20%
nuclear absorption
30–10%
ne
ne
Detector
 10–3
p–
DIF few %
nm
DAR 100%
+
m
capture90%
nm m–
DAR 10%
n m e+ n e
m– p  nm n
The only
nm e– ne source of
ne
Parameters of the LSND and KARMEN experiments
Accelerator
Proton kin. energy
Proton current
Detector
Detector mass
Event localisation
Distance from n source
Angle  between proton
and n direction
Data taking period
Protons on target
LSND
KARMEN
Los Alamos Neutron
Neutron Spallation Facility
Science Centre
ISIS ar R.A.L. (U.K.)
800 MeV
800 MeV
1000 mA
200 mA
Single cylindrical tank
filled with liquid scintillator
512 independent cells
Collect both scintillating
filled with liquid scintillator
and Čerenkov light
167 tons
56 tons
PMT timing
cell size
29 m
17 m
11°
90°
1993 – 98
4.6 x 1023
1997 – 2001
1.5 x 1023
Neutrino energy spectra from p+  m+ nm decay at rest
e+ nm ne
MeV
ne detection: the “classical” way
n e + p  e+ + n
delayed signal from np  gd (Eg = 2.2 MeV)
KARMEN has Gd-loaded paper between
adjacent cells  enhanced neutron capture,
SEg = 8.1 MeV
prompt signal
KARMEN beam time structure
Repetition rate 50 Hz
Expect nm  ne oscillation signal
within ~10 ms after beam pulse
LSND beam time structure
Repetition rate 120 Hz
0
time [ms]
600 ms
no correlation between event time
and beam pulse
LSND final results: evidence for nm – ne oscillations
Positrons with 20 < E < 200 MeV correlated in space and time with 2.2 MeV g-ray
from neutron capture:
N(beam-on events) – N(beam-off events) = 117. 9 ± 22.4 events
Background from DAR n = 29.5 ± 3.9
Background from DIF ne = 10.5 ± 4.6
ne signal = 87. 9 ± 22.4 ± 6.0 events
(stat.)
(syst.)
Posc( nm – ne) = (0.264 ± 0.067 ± 0.045) x 10-2
Tighter event selection (less background)
Positrons with 20 < E < 60 MeV
N(beam-on) – N(beam-off) = 49.1 ± 9.4 events
n-induced background = 16.9 ± 2.3
ne signal = 32.2 ± 9.4 events
KARMEN final results
Events selection criteria: space and time correlation between prompt and delayed signal;
time correlation between prompt signal and beam pulse;
16 < E(e+) < 50 MeV
Number of selected events = 15
Expected backgrounds:
Cosmic rays: 3.9 ± 0.2
Random coincidences between two ne  e– events: 5.1 ± 0.2
Random coincidences between ne  e– and uncorrelated g: 4.8 ± 0. 3
Intrinsic ne contamination: 2.0 ± 0. 2
Total background: 15.8 ± 0. 5 events
no evidence for nm – ne oscillations
Posc( nm – ne) < 0.085 x 10-2 (90% confidence)
LSND value: (0.264 ± 0.067 ± 0.045) x 10-2
Consistency between KARMEN and LSND
is only possible for a restricted region
of oscillation parameters because the baseline L
is different for the two experiments:
L = 29 m (LSND);
L = 17 m (KARMEN)
LSND allowed region and
KARMEN exclusion region
LSND evidence for nm – ne oscillations: a very serious problem
Define: mik2 = mk2 – mi2 (i,k = 1, 2, 3)
m122 + m232 + m312 = 0
Evidence for neutrino oscillations:
 Solar neutrinos:
m122  6.9 x 10–5 eV2
 Atmospheric neutrinos: m232  2.5 x 10–3 eV2
 LSND:
|m312| = 0.2 — 2 eV2
| m122 + m232 + m312 | = 0.2 — 2 eV2
If all three results are correct, at least one additional neutrino
is needed.
To be consistent with LEP results (only three neutrinos),
any additional neutrino, if it exists, must be “sterile”
(no coupling to W and Z bosons  no interaction with matter)
LSND result needs confirmation
MiniBooNE (Booster Neutrino Experiment at Fermilab)
Goal: to definitively confirm (or disprove) the LSND signal
 start with nm – ne appearance search;
 then search for nm – ne search;
 if a positive signal is found, build a second detector at different L
Beryllium
Fermilab
target
8 GeV proton
synchrotron
focuses p+ in an
almost parallel beam
Neutrino beam flux
calculations
450 m
earth
n flux
(arbitrary units)
50 m
decay
region
En [GeV]
MiniBooNE detector
 12 m diameter spherical tank
 807 tons mineral oil used as
Čerenkov radiator
 fiducial mass 445 tons
 optically isolated inner region
with 1280 20 cm diam. PM tubes
 external anticoincidence region
with 240 PM tubes
Particle identification:
based on different behaviour of electrons,
muons, pions and pattern of Čerenkov light rings
MiniBooNE expectations for two years of data taking (1021 protons on target)
~500K nmC  m–X events, ~70K nC  nX events
MiniBooNE exclusion region after
Background to the nm – ne oscillation signal:
two years of data taking
1500 neC  e– X events (from beam contamination)
if no oscillation signal is observed
500 mis-identified m–
500 mis-identified p°
+ 1000 neC  e– X events
if the LSND result is correct
LSND allowed
region:
90% C.L.
99% C.L.
Note: the electron energy distributions
from nm – ne oscillations and from
the ne contamination in the beam
are different because the nm
and contamination ne have
different energy spectra
Start data taking: June 2002
sin22
Long baseline experiments at accelerators
Super-K L/E distribution does not show
oscillatory behaviour expected from
oscillations because of poor resolution
on the L/E variable at large L/E values
Ideally:
Data
Prediction
Purpose: to provide definitive demonstration that the atmospheric nm deficit
is due to neutrino oscillations using accelerator-made nm .
Data
2
2
2 L
 1  sin (2) sin 1.27 m 
Prediction
E

Maximum L  12800 km
to study the region
L/E > 104 km need events with E < 1 GeV for which
the angular correlation between the incident neutrino and
the outgoing muon is weak
poor L/E resolution
L / E [km/GeV]
Planned measurements at long baseline accelerator experiments:
 Distortions of the nm energy spectrum at large distance (measurement of m2 and sin22);
 Ratio of neutral current to charged current events (to distinguish nm – nt oscillations
from oscillations to a “sterile” neutrino ns);
 nt appearance at large distance in a beam containing no nt at production.
Long baseline accelerator experiments
(in progress or in preparation)
Project
Baseline L
<En>
Status
K2K (KEK to KAMIOKA)
250 km
1.3 GeV
Data taking since June 99
MINOS (Fermilab to Soudan)
735 km
few GeV
Start data taking: 2005
CERN to Gran Sasso
732 km
17 GeV
Start data taking: 2006
 Threshold energy for nt + N  t– + X: En > 3.5 GeV
 Typical event rate ~1 nm  m– event / year per ton of detector mass
need detectors with masses of several kilotons
 nm beam angular divergence:
beam line

p+
p
0.03GeV
 T 
 3 mrad at 10 GeV
pL En [GeV ]
Beam transverse size: 100 m – 1 km at L > 100 km
no problems to hit the far detector
but neutrino flux decreases as L–2 at large L
nm from p+  m+ nm decay
K2K
Neutrino beam
composition:
95% nm
4% nm
1% ne
K2K Front Detector: neutrino flux
monitor and measurement of nm
interactions without oscillations
1 Kton Water Čerenkov detector:
Similar to Super-K;
fiducial mass 25 tons
Scintillating Fibre Water Detector
(SciFi):
Detect multi-track events;
fiducial mass 6 tons
Muon chambers:
Measure m range from p decay;
mass 700 tons; nm beam monitor
L=250 km
12 GeV
proton
synchrotron
1Rm: 1–ring m-like events
beam spill duration
Expected Posc(nm–nm) versus En at L = 250 km
for m2 = 3x10–3 eV2, sin22 = 1
Posc = 0
Expected shape of the nm spectrum
in Super-K with and without nm disappearance
En [GeV]
Beam–associated events in Super-K
June 1999 – July 2001 (4.8x1019 protons on target)
FCFV events, Evis > 30 MeV: Expected (Posc = 0): 80.1+6.2 events
–5.4
Observed: 56 events
(probability of a statistical fluctuation ~3% if Posc = 0)
Nov 1999 – July 2001 (stable beam conditions)
1Rm events:
Observed: 29 events
Measurement of the nm energy distribution in Super-K
using 1Rm events (assumed to be quasi-elastic events nm + n  m– + p)
m–
Incident nm
direction
(precisely known)

Recoil proton
(not detected because under
Čerenkov threshold)
Assume target neutron at rest and apply
two-body quasi–elastic kinematics to extract
incident nm energy:
Expected shape
(no oscillation)
Expected shape
for nm disappearance
m2 = 3x10–3 eV2
sin22 = 1 (Best fit)
MEm  0.5mm
En 
M  Em  pm cos
2
(M  nucleon mass)
Measured En distribution shows distortion
consistent with oscillation with m2 = 3x10–3 eV2,
sin22 = 1, as suggested by atmospheric neutrino data
Probability for no oscillation 0.7% (combining event
deficit and distortion of spectral shape)
En [GeV]
MINOS experiment
Neutrino beam from Fermilab
to Soudan (an inactive iron mine
in Minnesota): L = 730 km
Accelerator:
Fermilab Main Injector (MI)
120 GeV proton sinchrotron
High intensity (0.4 MW):
4x1013 protons per cycle
Repetition rate: 1.9 s
4x1020 protons on target / y
Hadron decay pipe: 700 m
MINOS Far Detector
 8 m octagonal steel tracking calorimeter
 Magnetized steel plates 2.54 cm thick
 4 cm wide scintillator strips between plates
 2 modules, each 15 m long
 5400 ton total mass (fiducial mass 3300 tons)
 484 planes of scintillator strips (26000 m2)
 Steel plates are magnetized: toroidal field,
B = 1.5 T
Far Detector is half-built, to be completed by
June 2003
Now recording cosmic ray events
MINOS Near Detector
 3.8x4.8 m “octagonal” steel tracking calorimeter
 Same basic construction as Far Detector
 282 magnetized steel plates
 980 ton total mass (fiducial mass 100 tons)
 installed 250 m downstream of the end of the decay pipe
First protons on target scheduled for December 2004
MINOS: Expected energy distributions for nm  m– events
Low energy beam, exposure of 10 kton x year
Histogram: no nm disappearance
Data points: oscillation with sin22 = 0.9
m2 is measured from position of minimum in the ratio versus E plot;
sin22 is measured from its depth.
MINOS: distinguishing between nm – nt and nm – ns oscillations
Compare ratio NC/CC defined as
Rate of muonless events
10 kton x year
Rate of m– events
in Far and Near Detector.
nm – nt oscillations:
nt is under threshold for t production
no charged current events;
same neutral current events as nm
 NC 
 NC 





 CC  Far  CC  Near
nm – ns oscillations:
ns does not interact with matter
no charged current events;
no neutral current events
 NC 
 NC 





 CC  Far  CC  Near
Beam energy:
Low
Medium
High
MINOS excluded region for nm – nt oscillations
if (NC/CC) is found to be the same within errors
in the Near and Far Detector
CNGS (CERN Neutrinos to Gran Sasso)
Search for nt appearance at L = 732 km
Expected number of nt + N  t – + X events (Nt):
Emax
Nt  A
Normalization constant:
contains detector mass,
running time, efficiencies,
etc.
F
m
( E )Pmt (E )s t ( E )dE
3.5GeV
nm flux
cross-section
for t– production
nm – nt oscillation probability Pmt:
L
 L
Pmt  sin 2 (2) sin 2 (1.27 m2 )  1.27 2 sin 2 (2)(m2 ) 2  
E
E
2
Good approximation for: L = 732 km, E > 3.5 GeV, m2 < 4x10–3 eV2
Emax
st ( E )
N t  1.61sin (2)( m ) L
Fm ( E )
dE
2
E
3.5GeV
2
2 2
2

Disadvantages:
L = 732 km is too short to reach the first nm – nt oscillation maximum
 Nt depends on (m2) 2
very low event rates at low values of m2
Advantages:
 Beam optimization does not depend on m2 value
400 GeV proton beam from
the CERN SPS
Neutrino beam
layout at CERN
Neutrino beam energy
spectra and interaction
rates at Gran Sasso
Primary protons:
400 GeV;
4x2.3x1013 / SPS cycle
SPS cycle: 26.4 s
Running efficiency 75%
Running time 200 days/year
Protons on target:
4.5 x 1019 / year
(sharing SPS with other users)
With SPS in dedicated mode (no other user) expect 7.6 x 1019 protons on target / year
Search for nt appearance at Gran Sasso
Two detectors (OPERA, ICARUS)
No near detector
Gran Sasso National Laboratory and the two neutrino detectors
OPERA experiment: t – detection through the observation of one-prong decays
Typical t mean decay length 1 mm
need very good space resolution
Use photographic emulsion (space resolution ~1 mm)
Plastic base
“Brick”: 56 emulsion films
separated by 1 mm thick Pb plates
packed under vacuum
50 mm thick emulsion films
Internal brick structure
Bricks are arranged into “walls” of 52 x 64 bricks
Walls are arranged into “supermodules”: 31 walls / supermodule
Two supermodules, each followed by a magnetic spectrometer
206 336 bricks, total mass 1800 tons
Track detectors (orthogonal planes of scintillator strips) are inserted among brick
walls to provide trigger and to identify the brick where the neutrino interaction
occurred. The brick is immediately removed for emulsion development and
automatic scanning and measurement using computer-controlled microscopes
OPERA supermodule
Magnetic spectrometer:
magnetized iron dipole
12 Fe plates
5 cm thick
equipped with
trackers (RPC)
OPERA: backgrounds and sensitivity
nm – nt oscillation signal
5 year run
1800 ton target mass
2.25x1020 protons on target
Exclusion regions
3 years
5 years
ICARUS: a novel detector based on
a liquid Argon Time Projection Chamber
(TPC)
Detect primary ionization in Argon
3-dimensional event reconstruction
with space resolution ~1 mm
Excellent calorimetric energy resolution
for hadronic and electromagnetic
showers
UV scintillation light emitted in Argon
is collected by PM tubes to provide
a t=0 signal
Electrodes at
negative high
voltage
Drift field: 1 kV/cm
Drift times > 3 ms
Measurement of coordinates:
x, z: charge-collecting electrodes
(wires planes)
y: drift time
A 600 Ton module (T600) is operational;
installation at Gran Sasso starts in 2003
Cryostat length along z: 19.6 m
Charge-collecting electrodes
Some events detected by T600
Cosmic
muon
with
-rays
Hadron interaction
Muon decay
at rest
Electromagnetic shower
T3000 ICARUS Detector (proposed, operational by Summer 2006)
~70 m
3000 tons, 2350 tons of active Argon target
Physics topics to be addressed by ICARUS T3000
 Solar neutrinos
 Atmospheric neutrinos
 Supernova neutrinos
 CNGS beam neutrinos
 Proton decay
ICARUS T3000: search for nt appearance in the t –  nt e– ne decay channel
Main background source: ne + N  e– + X (from the <1% ne contamination in the beam)
Use kinematic criteria to separate signal from background:
 Beam ne have harder spectrum than nm
signal has lower visible energy
 Signal has two invisible neutrinos in the final state
larger missing transverse
momentum
Expected distributions for 2.25 x 1020 protons on target (5 years of data taking)
Final signal selection is based on 3-dimensional likelihood using three variables
with different distributions for signal and background:
 visible energy Evis
 missing transverse momentum pTmiss
 r = pTe / (pTe + pThad + pTmiss)
For each event define two likelihoods:
 Likelihood to be a signal event LS(Evis , pTmiss, r)
 Likelihood to be a background event LB(Evis , pTmiss, r)
Define l = LS/LB
Expected signal event rates and background
t  e signal
m2=1.6x10–3 eV2 m2=2.5x10–3 eV2 m2=3.0x10–3 eV2 m2=4.0x10–3 eV2 Background
3.7
9.0
13.0
for 2.25x1020 protons on target (5 years of data taking)
Same sensitivity as OPERA
23.0
0.7
Short baseline searches for nm – nt oscillations
CHORUS and NOMAD experiments at CERN (approved in 1992 to verify the hypothesis
that nt was an important component of dark matter with a mass  few eV)
The SPS Neutrino Beam from 1992 to 1998
Target: 800 kg of fully sensitive emulsion
Fibre tracker: high resolution tracker
to localize neutrino event in emulsion
Magnetic spectrometers and calorimeters: to measure secondary particle momentum
and energy
NOMAD detector
electron/hadron
separation
Momentum resolution: p/p = ±3.5% for p < 10 GeV/c
Electromagnetic Calorimeter resolution:
s E 3. 2 %

 1% (E in GeV)
E
E
Three typical NOMAD events
nm + N  m– + hadrons
m– track
ne + N  e– + hadrons
Electromagnetic
calorimeter
signal amplitude
ne + N  e+ + hadrons
CHORUS: t – detection through the observation of one-prong decays
Neutrino event vertex reconstruction with sub-mm resolution
Scan secondary tracks for decay “kink” near the event vertex
1m events (candidates for t –  m– decay)
Expected for sin22=1 and m2> 50 eV2:
5014 events
Expected background:
0.1
Observed:
0
0m events (candidates for t –  h– decay)
Expected for sin22=1 and m2> 50 eV2:
2004 events
Expected background:
1.1
Observed:
0
NOMAD: t – detection using kinematic criteria
t –  e– candidates
Expected for sin22=1 and m2> 50 eV2:
Expected background:
Observed:
t –  h– candidates
Expected for sin22=1 and m2> 50 eV2:
Expected background:
Observed:
t –  (h– h– h+) candidates
Expected for sin22=1 and m2> 50 eV2:
Expected background:
Observed:
2826 events
0.61
0
5343 events
0.76
1
675 events
0.32
0
No evidence
for nm – nt
oscillations
m2 [eV2]
Final CHORUS & NOMAD
exclusion regions
for nm – nt oscillation
CHORUS result:
two different statistical methods
T. Junk
Feldman & Cousins
Combined result uses the
Feldman & Cousins method
CHORUS, NOMAD:
the most sensitive oscillation
search experiments done so far.
However, the m2 value driving
nm – nt oscillations (m2  2.5x10–3 eV2)
is much lower than anticipated in 1992
sin22
LONG–TERM FUTURE
 Precise measurement of the neutrino mixing matrix
 Detect CP violating effects in neutrino oscillations
Assumptions: LSND result will NOT be confirmed
only three neutrinos
m1 < m2 < m3 ; two independent m2 values
m22 – m12  12 = (0. 3 — 2)x10–4 eV2 (oscillations of solar neutrinos)
m32 – m22  23 = (1.3 — 3.9)x10–3 eV2 (oscillations of atmospheric neutrinos)
Oscillations among three neutrinos are described by three angles (12, 13, 23)
and one CP-violating phase ():
c12 c13
n e  
  
i
n


c
s
e
 m   23 12  c12 s13 s23
 n   s s e i  c c s
 t   12 23
12 23 13
c13 s12
c12 c23ei  s12 s13 s23
 c12 s23ei  c23 s12 s13
s13 n 1 
 
c13 s23 n 2 
c13c23 n 3 
(cik  cosik; sik  sinik )
Present experimental information:
1. Solar neutrinos: ne disappearance driven by 12, large mixing (27° < 12 < 39°)
2. Atmospheric neutrinos: nm disappearance driven by 23, large mixing (37° < 23 < 53°)
3. CHOOZ nuclear reactor experiment: no evidence for ne disappearance driven by 23
Constraints from the CHOOZ experiment for three–neutrino mixing
Formalism can be simplified because 12 << 23 (32/12  10)
Oscillation lengths in the CHOOZ experiment (<E>  3 MeV, L  1000 m):
l12  2.54
E
 36000 m  L
12
l 23  2.54
E
 3000 m (50%)
 23
comparable to L
neglect oscillation terms driven by 12 ( set L/l12 = 0 in all formulae)
ne disappearance probability in the CHOOZ experiment:
Posc (n e n e )  1  sin 2 213 sin 2 (1.27 23
L
)
E
CHOOZ limit: sin2213 < 0.12 at 23  2.5x10–3 eV2
(identical to two-neutrino mixing)
13 < 10°
CP violation for three–neutrino mixing
CP violation: Posc(n – nb)  Posc( n – nb )
CPT invariance: Posc(n – nb) = Posc( nb – n ) (, b = e, m, t neutrino flavour index)
Posc(n – n) = Posc( n – n ) because of CPT invariance
CP violation in neutrino oscillations can only be measured in
appearance experiments
Measuring CP violation effects in neutrino oscillations requires neutrino beams
at least 100 times more intense than existing ones.
NEUTRINO FACTORY: a muon storage ring with long straight sections
pointing to neutrino detectors at large distance. Stored muons: 1021 per year
Components of a Neutrino Factory:
 A very high intensity proton accelerator. Beam intensity up to 1015 protons/s,
energy few GeV ;
 A large aperture magnetic channel located immediately after the proton target
to capture p± from the target and m± from p± decay;
 Muon “cooling” to reduce the muon beam angular and momentum spread;
 Two or more muon accelerators in series;
 A muon storage ring with long straight sections.
Stored m+  pure nm and ne beams
Stored m–  pure nm and ne beams
Fluxes and energy spectra precisely calculable from m decay kinematics
Search for ne – nm oscillations:
Detection of “wrong sign” muons (charge sign opposite to stored muons)
need magnetic detector
A possible scheme for a Neutrino Factory
long 20 cm aperture
superconductive solenoid
B = 10 T
Intense R&D program
on Neutrino Factories
in progress, but no proposal yet.
Muon cooling
In the transverse plane: successive stages of acceleration and ionization loss
initial
muon
momentum
LiH RF cavity
absorber
reduces pm
Acceleration increases only
the longitudinal momentum
component  reduce
angle to beam line
In the longitudinal plane:
Use RF cavity with time–modulated amplitude:
Small amplitude for early (fast) muons;
Large amplitude for late (slow) muons
Expected neutrino fluxes
(particles / (year x 0.25 GeV)
through a 10 m diameter
detector at L = 732 km;
m+ with Em = 10, 20, 50 GeV
beam line
CP violation in ne – nm oscillations
Definition: Pem  Posc(ne – nm) ; Pem  Posc(ne – nm)
L
L
L
L
L
Pem  Asin 2 (1.27 23 )  B sin 2 (1.2712 )  C cos(  1.27 23 ) sin(1.27 23 ) sin(1.2712 )
E
E
E
E
E
L
L
L
L
L
Pem  Asin 2 (1.2723 )  B sin 2 (1.2712 )  C cos(  1.2723 ) sin(1.2723 ) sin(1.2712 )
E
E
E
E
E
A = (sin23 sin213 )2
B = (cos23 sin212 )2
C = cos13 sin212 sin213 sin223
CP violating terms (note sign of phase )
CP violation in neutrino oscillations is measurable only if 13  0
AND the experiment is sensitive to BOTH 12 and 23
A ne oscillation experiment with much higher sensitivity than CHOOZ
is needed to measure 13
Disappearance experiments at nuclear reactors are systematically limited
by the uncertainty on the ne flux (± 2.7%)
need a nm – ne appearance experiment with very high sensitivity (Posc sin2213)
A high sensitivity nm – ne oscillation experiment requires a detector located near the first
oscillation maximum of 23. Existing experiments need a low energy neutrino beam.
K2K:
neutrino flux too low despite large detector mass (Super-K)
CNGS: program optimized for nt appearance (beam energy above threshold for
t production, too high for a nm – ne oscillation search), no near detector to measure
the intrinsic ne contamination in beam
MINOS: expect marginal improvement with respect to CHOOZ
MINOS
Future facilities (before building a
full Neutrino Factory)
JHF: a high intensity 50 GeV proton
synchrotron in Japan scheduled to start
in 2006. Can measure sin213 with high
sensitivity by aiming a neutrino beam
at Super-K (L = 270 km)
CHOOZ
sin213
Measurement of CP violation with a Neutrino Factory
Problem #1: sensitivity decreases rapidly with decreasing 13
No sensitivity to phase  for 13 < 1°
Problem #2: Optimal L to measure  is several 1000 km
neutrino beam traverses the Earth°
Matter effects have opposite sign for neutrino and antineutrino
apparent CP violation
Solution to problem #2: Matter effects and true CP violation in the mixing matrix
have different E and L dependence
take data with
two detectors at different distances and study effect as a
function of E
Expected number of events per year in a 40 kton detector for 2.5x1020 m+ decays
in the straight section of a 50 GeV Neutrino Factory:
L [km]
nmNm+X
neNe–X
nNnX
730
8.8x106
1.5x107
8x106
3500
3x105
6x105
3x105
7000
3x104
1. 3x105
5x104
CONCLUSIONS
 Convincing evidence for neutrino oscillations from solar and atmospheric
neutrino experiments
evidence for neutrino mixing (not yet included
in the Standard Model)
 Do sterile neutrinos exist? Wait for MiniBooNE results to confirm or disprove
the LSND evidence for nm – ne oscillation [presumably, if sterile neutrinos
exist, there is more than one (one for each family?)]
 Assume no sterile neutrino exists (wrong LSND result) and m1 << m2 << m3:
then m22  12 and m32  23
m2 = ( 0.5 – 1.4)x10–2 eV; m3 = 0.04 – 0.06 eV
unless neutrinos are mass degenerate (m >> m), they are only a small
component of dark matter in the Universe
 Mixing angles are found to be much larger in the neutrino sector than in
the quark sector. Data are consistent with maximal mixing for atmospheric nm
(23  45°), while the largest quark mixing angle is 13° (the Cabibbo angle)
 Present data suggest: ne consists mainly of n1 and n2, with little (zero?) n3;
nm and nt are ~50% n3 and the remainder is the state
orthogonal to ne
 How big is the n3 component of ne? Sensitive measurements of 13 must receive
very high priority. The long term future of neutrino physics depends on
the magnitude of 13
 Neutrino Factories appear to be the only way to study CP violation in the
neutrino sector. Are they feasible? Are they affordable? Need more R&D
to answer.